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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "x = 5\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e908c610-e60a-439a-9f2f-5f889c56cf7f",
   "metadata": {},
   "source": [
    "# 示例 Markdown 文档\n",
    "\n",
    "这是一个简单的 Markdown 示例，展示了 Markdown 的基本用法。\n",
    "\n",
    "## 标题\n",
    "Markdown 支持六级标题，从一级标题到六级标题，分别使用不同数量的井号 `#` 来表示。\n",
    "\n",
    "### 二级标题\n",
    "#### 三级标题\n",
    "##### 四级标题\n",
    "###### 五级标题\n",
    "###### 六级标题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3344638-acf8-4f25-926c-6cf27f843e34",
   "metadata": {},
   "source": [
    "## 段落\n",
    "Markdown 中的段落就是普通的文本，段落之间使用空行分隔。\n",
    "\n",
    "这是第一段。\n",
    "\n",
    "这是第二段。\n",
    "\n",
    "## 列表\n",
    "### 无序列表\n",
    "无序列表使用 `-`、`+` 或 `*` 作为列表项的标记。\n",
    "- 列表项 1\n",
    "- 列表项 2\n",
    "  - 子列表项 1\n",
    "  - 子列表项 2\n",
    "\n",
    "### 有序列表\n",
    "有序列表使用数字和点号 `.` 作为列表项的标记。\n",
    "1. 列表项 1\n",
    "2. 列表项 2\n",
    "   1. 子列表项 1\n",
    "   2. 子列表项 2\n",
    "\n",
    "## 链接\n",
    "链接可以使用行内式或参考式两种方式来创建。\n",
    "\n",
    "### 行内式链接\n",
    "[百度](https://www.baidu.com)\n",
    "\n",
    "### 参考式链接\n",
    "我经常访问 [百度][1]。\n",
    "\n",
    "[1]: https://www.baidu.com\n",
    "\n",
    "## 图片\n",
    "图片的语法和链接类似，只是在前面加一个感叹号 `!`。\n",
    "\n",
    "![示例图片](https://picsum.photos/200/300)\n",
    "\n",
    "## 代码块\n",
    "### 行内代码\n",
    "使用反引号 ` 包裹行内代码，例如 `print(\"Hello, World!\")`。\n",
    "\n",
    "### 代码块\n",
    "使用三个反引号 ``` 包裹代码块，并可以指定代码的语言。\n",
    "\n",
    "```python\n",
    "def hello():\n",
    "    print(\"Hello, World!\")\n",
    "\n",
    "hello()"
   ]
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   "cell_type": "markdown",
   "id": "a0e32cee-609f-4aad-aa23-3c1e11dc7f8d",
   "metadata": {},
   "source": [
    "\n",
    "\\section{微积分公式}\n",
    "牛顿 - 莱布尼茨公式：\n",
    "\\[\n",
    "\\int_{a}^{b} f(x) \\mathrm{d}x = F(b) - F(a)\n",
    "\\]\n",
    "其中 \\(F(x)\\) 是 \\(f(x)\\) 的一个原函数，即 \\(F'(x)=f(x)\\)。\n",
    "\n",
    "多元函数的泰勒展开式：设 \\(z = f(x,y)\\) 在点 \\((x_0,y_0)\\) 的某邻域内具有直到 \\(n + 1\\) 阶的连续偏导数，则对该邻域内任一 点 \\((x,y)=(x_0+\\Delta x,y_0+\\Delta y)\\) 有\n",
    "\\[\n",
    "f(x,y)=f(x_0,y_0)+\\sum_{i = 1}^{n}\\frac{1}{i!}\\left(\\Delta x\\frac{\\partial}{\\partial x}+\\Delta y\\frac{\\partial}{\\partial y}\\right)^i f(x_0,y_0)+R_n\n",
    "\\]\n",
    "其中 \\(R_n=\\frac{1}{(n + 1)!}\\left(\\Delta x\\frac{\\partial}{\\partial x}+\\Delta y\\frac{\\partial}{\\partial y}\\right)^{n+1}f(x_0+\\theta\\Delta x,y_0+\\theta\\Delta y)\\)，\\(0<\\theta<1\\)。\n",
    "\n",
    "\\section{线性代数公式}\n",
    "矩阵的特征值和特征向量满足：\n",
    "\\[\n",
    "A\\mathbf{v}=\\lambda\\mathbf{v}\n",
    "\\]\n",
    "其中 \\(A\\) 是 \\(n\\times n\\) 矩阵，\\(\\mathbf{v}\\) 是 \\(n\\) 维非零列向量，\\(\\lambda\\) 是标量，称为矩阵 \\(A\\) 的特征值，\\(\\mathbf{v}\\) 称为属于特征值 \\(\\lambda\\) 的特征向量。\n",
    "\n",
    "矩阵的行列式（以 \\(3\\times3\\) 矩阵为例）：\n",
    "\\[\n",
    "\\det(A)=\\begin{vmatrix}\n",
    "a_{11}&a_{12}&a_{13}\\\\\n",
    "a_{21}&a_{22}&a_{23}\\\\\n",
    "a_{31}&a_{32}&a_{33}\n",
    "\\end{vmatrix}=a_{11}\\begin{vmatrix}\n",
    "a_{22}&a_{23}\\\\\n",
    "a_{32}&a_{33}\n",
    "\\end{vmatrix}-a_{12}\\begin{vmatrix}\n",
    "a_{21}&a_{23}\\\\\n",
    "a_{31}&a_{33}\n",
    "\\end{vmatrix}+a_{13}\\begin{vmatrix}\n",
    "a_{21}&a_{22}\\\\\n",
    "a_{31}&a_{32}\n",
    "\\end{vmatrix}\n",
    "\\]\n",
    "\n",
    "\\section{概率论公式}\n",
    "正态分布的概率密度函数：\n",
    "\\[\n",
    "f(x)=\\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}\n",
    "\\]\n",
    "其中 \\(\\mu\\) 是均值，\\(\\sigma\\) 是标准差。\n",
    "\n",
    "条件概率公式：\n",
    "\\[\n",
    "P(A|B)=\\frac{P(A\\cap B)}{P(B)}\n",
    "\\]\n",
    "其中 \\(P(A|B)\\) 表示在事件 \\(B\\) 发生的条件下事件 \\(A\\) 发生的概率，\\(P(A\\cap B)\\) 是事件 \\(A\\) 和 \\(B\\) 同时发生的概率，\\(P(B)>0\\)。\n",
    "\n"
   ]
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  {
   "cell_type": "markdown",
   "id": "cdc009eb-b2ad-4350-bf52-549263fe778c",
   "metadata": {},
   "source": [
    "# 微积分公式\n",
    "牛顿 - 莱布尼茨公式：\n",
    "$$\n",
    "\\int_{a}^{b} f(x) \\mathrm{d}x = F(b) - F(a)\n",
    "$$\n",
    "其中 \\(F(x)\\) 是 \\(f(x)\\) 的一个原函数，即 \\(F'(x)=f(x)\\)。\n",
    "\n",
    "多元函数的泰勒展开式：设 \\(z = f(x,y)\\) 在点 \\((x_0,y_0)\\) 的某邻域内具有直到 \\(n + 1\\) 阶的连续偏导数，则对该邻域内任一 点 \\((x,y)=(x_0+\\Delta x,y_0+\\Delta y)\\) 有\n",
    "$$\n",
    "f(x,y)=f(x_0,y_0)+\\sum_{i = 1}^{n}\\frac{1}{i!}\\left(\\Delta x\\frac{\\partial}{\\partial x}+\\Delta y\\frac{\\partial}{\\partial y}\\right)^i f(x_0,y_0)+R_n\n",
    "$$\n",
    "其中 \\(R_n=\\frac{1}{(n + 1)!}\\left(\\Delta x\\frac{\\partial}{\\partial x}+\\Delta y\\frac{\\partial}{\\partial y}\\right)^{n+1}f(x_0+\\theta\\Delta x,y_0+\\theta\\Delta y)\\)，\\(0<\\theta<1\\)。\n",
    "\n",
    "# 线性代数公式\n",
    "矩阵的特征值和特征向量满足：\n",
    "$$\n",
    "A\\mathbf{v}=\\lambda\\mathbf{v}\n",
    "$$\n",
    "其中 \\(A\\) 是 \\(n\\times n\\) 矩阵，\\(\\mathbf{v}\\) 是 \\(n\\) 维非零列向量，\\(\\lambda\\) 是标量，称为矩阵 \\(A\\) 的特征值，\\(\\mathbf{v}\\) 称为属于特征值 \\(\\lambda\\) 的特征向量。\n",
    "\n",
    "矩阵的行列式（以 \\(3\\times3\\) 矩阵为例）：\n",
    "$$\n",
    "\\det(A)=\\begin{vmatrix}\n",
    "a_{11}&a_{12}&a_{13}\\\\\n",
    "a_{21}&a_{22}&a_{23}\\\\\n",
    "a_{31}&a_{32}&a_{33}\n",
    "\\end{vmatrix}=a_{11}\\begin{vmatrix}\n",
    "a_{22}&a_{23}\\\\\n",
    "a_{32}&a_{33}\n",
    "\\end{vmatrix}-a_{12}\\begin{vmatrix}\n",
    "a_{21}&a_{23}\\\\\n",
    "a_{31}&a_{33}\n",
    "\\end{vmatrix}+a_{13}\\begin{vmatrix}\n",
    "a_{21}&a_{22}\\\\\n",
    "a_{31}&a_{32}\n",
    "\\end{vmatrix}\n",
    "$$\n",
    "\n",
    "# 概率论公式\n",
    "正态分布的概率密度函数：\n",
    "$$\n",
    "f(x)=\\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}\n",
    "$$\n",
    "其中 \\(\\mu\\) 是均值，\\(\\sigma\\) 是标准差。\n",
    "\n",
    "条件概率公式：\n",
    "$$\n",
    "P(A|B)=\\frac{P(A\\cap B)}{P(B)}\n",
    "$$\n",
    "其中 \\(P(A|B)\\) 表示在事件 \\(B\\) 发生的条件下事件 \\(A\\) 发生的概率，\\(P(A\\cap B)\\) 是事件 \\(A\\) 和 \\(B\\) 同时发生的概率，\\(P(B)>0\\)。"
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